Thanks Kashish - I can't see any details re: my query here though?
Can you please try these steps:
1. From the Server Menu -> Sign In option -> Sign out (not from the workbook's bottom sign-out)
2. From the Server Menu -> Sign In -> type the website as: https://public.tableau.com/
If it does not ask for your credentials, which happens mostly when sign-out and sign-in immediately back, then make sure you sign-out again as in step 1.
(This is the most important step which I noticed during my ordeal for around 3 hours)
3. Provide your credentials again to sign-in
4. Now Save the workbook either using Server -> Tableau Public -> Save to or Save As option.
I tested these steps for the first time publish as well as after publishing -> making changes.
thanks for you help! Unfortunately this did not work. I think it might be a local problem - I have edited above.
I had another trick which worked for the same error. But it works only if you have the workbook already published earlier and when you are trying to re-publish it later. I have tested this using Tableau Desktop not Tableau Public software.
The trick is to download the published file and open that published file in Desktop. Publish the same downloaded file without any changes again to Tableau Public. If this get's published successfully (which it should), then without closing it or signing out, make the required changes/updates to this workbook and republish again to Tableau Public.